The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A066230 f-perfect numbers defined by f(n) = n - 1 (where f-perfect numbers are defined in A066218). 4
 1, 12, 196, 368, 1696, 30848, 437745, 2075648, 8341504, 33452032, 34355150848 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equivalently, let g(n) = sigma(n)-n-d(n)+2, where d(n) is the number of divisors of n and sigma(n) is their sum. Then n is in the sequence if g(n)=n. It seems that if 2^(i+1)-(2*i+1) is prime, 2^i*(2^(i+1)-(2*i+1)) is in the list. For example i in {2, 4, 5, 7, 10, 11, 12, 17, 24, 30, 34, 113, 151, 185}. No other exceptions than 1, 196 and 437745 for n < 10^8. - Lambert Klasen (lambert.klasen(AT)gmx.net), Jul 31 2005 If 2^(i + 1)-(2i + 1) is prime then n = 2^i*(2^(i + 1)-(2i + 1)) is in the sequence because sigma(n)-d(n) + 2 = (2^(i + 1)-1)*(2^(i + 1)-2i)-2(i + 1) + 2 = 2^(i + 1)*(2^(i + 1)-(2i + 1)) = 2n, so sigma(n)-n-d(n) + 2 = n. -Farideh Firoozbakht, Sep 18 2006 a(12) > 2*10^11. - Donovan Johnson, Jun 25 2012 a(12) > 10^13. - Giovanni Resta, Aug 21 2013 LINKS J. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (2002-2003), 168-172. EXAMPLE f(12) = 11 = 0 + 1 + 2 + 3 + 5 = f(1) + f(2) + f(3) + f(4) + f(6), hence 12 is a term of the sequence. MATHEMATICA g[ n_ ] := DivisorSigma[ 1, n ]-n-DivisorSigma[ 0, n ]+2; For[ n=1, True, n++, If[ g[ n ]==n, Print[ n ] ] ] CROSSREFS Cf. A066218, A066511, A066229. Sequence in context: A296942 A159498 A034671 * A262845 A321033 A048667 Adjacent sequences:  A066227 A066228 A066229 * A066231 A066232 A066233 KEYWORD nonn,more AUTHOR Joseph L. Pe, Dec 18 2001 EXTENSIONS Edited by Dean Hickerson, Jan 10, 2002. More terms from Jason Earls, May 14 2002 2 more terms from Farideh Firoozbakht, Sep 18 2006 a(11) from Donovan Johnson, Jun 25 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 8 12:28 EST 2021. Contains 349596 sequences. (Running on oeis4.)